# 12.2.1: Wind axes-Local horizon orientation

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To situate the wind axis reference frame with respect to the local horizon reference frame, the general form given in Example (12.2) is particularized for:

• $$F_I \equiv F_h; F_F \equiv F_w,$$
• $$\delta_3 \equiv \chi \to \text{Yaw angle,}$$
• $$\delta_2 \equiv \gamma \to \text{Flight path angle,}$$
• $$\delta_1 = \equiv \mu \to \text{Bank angle}.$$

The transformation matrix will be:

$L_{wh} = \begin{bmatrix} \cos \gamma \cos \chi & \cos \gamma \sin \chi & - \sin \gamma \\ \sin \mu \sin \gamma \cos \chi - \cos \mu \sin \chi & \sin \mu \sin \gamma \sin \chi + \cos \mu \cos \chi & \sin \mu \cos \gamma \\ \cos \mu \sin \gamma \cos \chi + \sin \mu \sin \chi & \cos \mu \sin \gamma \sin \chi - \sin \mu \cos \chi & \cos \mu \cos \gamma \end{bmatrix}.$

12.2.1: Wind axes-Local horizon orientation is shared under a CC BY-SA 3.0 license and was authored, remixed, and/or curated by Manuel Soler Arnedo via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.